Numerical Investigation of Natural Convention to a Pseudoplastic Fluid in a Long Channel using a Semi-Implicit Scheme

Abstract

We develop and computationally analyze a mathematical model for natural convection to a non-Newtonian fluid in a long and thin channel. The channel is bounded by antisymmetric heated and cooled walls and encloses a non-Newtonian pseudoplastic fluid. The flow and heat transfer characteristics are investigated subject to the prevailing buoyancy forces resulting from the combined natural convection and gravitational effects. An efficient and accurate semi-implicit finite difference algorithm is implemented in time and space to analyse the model equations. In the case when the fluid flow and heat transfer are sustained for a long enough time to allow for steady states to develop, the model equations would reduce to a boundary value problem. Even in such cases, we demonstrate that, by recasting the problem as an initial boundary value problem, our numerical algorithms would still converge in time to the relevant, steady-state solutions of the original boundary value problem. We also demonstrate the dependence of solutions on the embedded parameters at a steady state.